GCF of 431/197, 520/209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 431/197, 520/209 i.e 1/41173 easily. The following is the detailed procedure to determine the greatest common factor of fractions 431/197, 520/209.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 431/197,520/209?
Given fractions are 431/197,520/209
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 431/197,520/209, numerators are 431,520
Denominators are 197,209
The GCF of 431,520 is 1 .
LCM of 197,209 is 41173.
The greatest common factor of 431/197,520/209 = [GCF of 431,520]/[LCM of 197,209]= 1/41173
Therefore, the GCF of 431/197,520/209 is 1/41173.
To find the highest common factor of 431,520, we have to find the factors of both numbers and list the highest common factor.
The factors of 431 are 1, 431
The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520
The HCF of 431,520 is 1.
Lets's calculate GCF of 431,520
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 431,520 By Matching Biggest Common Factor Method
Now, list down the factors of 431
:1,431
Now, list down the factors of 520
:1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520
Greatest Common Factor
We found the factors 431,520 . The biggest common factor number is the GCF number.
So the greatest common factor 431,520 is 1.
Lets's calculate LCM of 197,209
Given numbers has no common factors except 1. So, there LCM is their product i.e 41173
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/41173
Therefore, the GCF of Fractions 431/197,520/209 is 1/41173
Least Common Multiple of 197,209 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 197,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(197,209) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(197,209) x common factors =1 x 1 = 1
LCM(197,209) = ( 197 × 209 ) / 1
LCM(197,209) = 41173 / 1
LCM(197,209) = 41173
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FAQs on GCF of Fractions of 431/197, 520/209
1. What is the HCF of 431,520?
The HCF of 431,520 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 431/197, 520/209?
Answer: GCF of Numerators as per given numbers 431/197, 520/209 is
GCF of Numerators i.e. for 431,520 is 1
LCM of denominators i.e. for 197,209 is 41173.
Thus, GCF of Fractions is 1/41173.Finally, GCF of Fractions for 431/197, 520/209 is 1/41173.